For a small extra premium most companies let you protect your no claims discount. However you need to check to see if this is transferable to another low cost simple car insurance quote if you choose to move company at a later date.
Young drivers under twenty five could consider being placed on their parent's policy as a named driver, as insurance costs for young drivers can be high. However in most cases they will not be able to build up their own no claims bonus. Some insurers will not insure someone who is not the registered owner of the car also.
When making a claim have as many details with you as possible including your policy number and a crime reference number if you have one.
If you own a "classic car" you may be able to get cheap insurance if you only do limited mileage each year. Often many companies have special rates for thsi type of vehicle especially if it is not your main car.